Stability analysis of the Crank-Nicolson-leapfrog method with the Robert-Asselin-Williams time filter

DOI10.1007/s10543-014-0493-1zbMath1325.65113OpenAlexW2037403470MaRDI QIDQ486708

Nicholas Hurl, Yong Li, William J. Layton, Cǎ tǎ lin Trenchea

Publication date: 16 January 2015

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-014-0493-1

zbMATH Keywords

Crank-Nicolson leaprog methodmultivalue methodRobert-Asselin-Williams filterstability bands

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (17)

Tensor methods for the Boltzmann-BGK equation ⋮ The Williams step increases the stability and accuracy of the hoRA time filter ⋮ A higher-order Robert-Asselin type time filter ⋮ Stability and convergence analysis of a Crank-Nicolson leap-frog scheme for the unsteady incompressible Navier-Stokes equations ⋮ A family of second order time stepping methods for the Darcy-Brinkman equations ⋮ A second order ensemble algorithm for computing the Navier-Stokes equations ⋮ A fully-decoupled artificial compressible Crank-Nicolson-leapfrog time stepping scheme for the phase field model of two-phase incompressible flows ⋮ High-Order Adaptive Time Stepping for the Incompressible Navier--Stokes Equations ⋮ Stabilized Richardson leapfrog scheme in explicit stepwise computation of forward or backward nonlinear parabolic equations ⋮ A second order, linear, unconditionally stable, Crank-Nicolson-Leapfrog scheme for phase field models of two-phase incompressible flows ⋮ Recent developments in IMEX methods with time filters for systems of evolution equations ⋮ A Crank-Nicolson leapfrog stabilization: unconditional stability and two applications ⋮ A conservative, second order, unconditionally stable artificial compression method ⋮ An optimally accurate discrete regularization for second order timestepping methods for Navier-Stokes equations ⋮ Crank-Nicolson leap-frog time stepping decoupled scheme for the fluid-fluid interaction problems ⋮ Three linear, unconditionally stable, second order decoupling methods for the Allen-Cahn-Navier-Stokes phase field model ⋮ Stabilized leapfrog scheme run backward in time, and the explicit O(Δ t)² stepwise computation of ill-posed time-reversed 2D Navier–Stokes equations

Cites Work

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• On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation
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